By definition, blood pressure is the force exerted by the blood on the walls of the blood vessels per unit area. So high blood pressure means that your blood is exerting more force per unit area on walls of your blood vessels. Most common cause of high blood pressure is atherosclerosis (normally occurs in old age). Atherosclerosis means hardening of your blood vessels, your blood vessels loose the elasticity. So when blood rushes with great velocity and force in blood vessels (especially arteries) the loss of elasticity of blood vessels prevent them to expand and in this way with less volume available, the force per unit area of blood on blood vessels is increases.
I think I have made it a little complicated. Let me explain what normally happens. During systole when the heart pushes blood into arteries, the amount of blood, force behind the blood and its velocity are all greater than can be accommodated in arteries, so to accommodate the extra amount of blood, the arteries expand (and that is what is called pulse). Then during diastole, when heart is not pumping any blood, the arteries return to their normal state and the extra blood flows into circulation. This all happens too quickly, (0.8 second for all the effects to take place). So the arteries because of their elasticity, eliminate the extra force of blood but in atherosclerosis, the elasticity is lost and arteries cannot expand so not only the force per unit area is increased but the rate of flow of blood is also increased.
The consequences of high blood pressure include the rupturing of blood vessels. failure of organs like the kidneys and heart failure. If you want me to explain why these occur with high blood pressure, let me know.